This thesis reports a study in the area of active vibration damping focused primarily on reconfiguration of control actuators following failure of one or more components. Several related issues concerning practical implementation were considered, and these also were discussed. These subjects were studied with reference to a particular laboratory structure, a hanging plane grid in the Spacecraft Controls Branch at NASA Langley Research Center. The structure had dynamics representative in many respects of a large, highly flexible space structure (LSS), and this study was intended to contribute toward the development of vibration control for LSS. A numerical analysis of the reconfiguration by computer simulation is presented. The possible future experimental validation of this numerical analysis motivated examination of some auxiliary problems related to implementation of vibration control with real, nonideal hardware. One of these problems is the effect of the dynamics of real sensors, actuators, and filters on a vibration control system. An experimental analysis of this problem was conducted, and the results presented here include hardware induced performance degradation and system instability. Another problem considered is prediction of response for use in feedback control by a digital controller that introduces a significant computational delay. A prediction technique is described, and some results of open-loop experimental evaluation of this technique are presented. Also, a computer simulation of closed-loop application of this technique was conducted, and the results, which include system instabilities, are presented. / M.S.

The presented work is intended to develop a geometrically reduced order (homogenized) model for a large antenna space structure with flexible joints. An energy equivalence concept is employed to find the continuum model for the system. The kinetic and strain energy expressions of the fundamental elements are found based on the assumptions of the micropolar elasticity theory. Necessary assumptions are made to reduce the order of the strain variables while retaining the effects of the micro-rotations that are coupled to the primary strain terms. As a result, a micropolar-based continuum model is found for the structure with torsional joints. The vibrations equations of motion for various coordinates of the one dimensional equivalent model are presented. Subsequently, the relations between the physical parameters of the distributed parameter model and the radar structure are introduced. The effect of the asymmetric mass distribution as a result of the addition of the radar panel to the truss system is studied. For the purpose of the experimental validation of the suggested model a planar truss structure with Pratt Girder configuration was built and tested in the laboratory. The results for the experimental frequency response functions are shown to be in good agreement with the theory. Finally, the continuum model is used to quantify the effects of the thermally induced disturbances on the satellite system during the eclipse transition. / Ph. D.

During the past decade, researchers have shown much interest in control and identification of Large Space Structures (LSS). Our inability to model these LSS accurately has generated extensive research into robust controllers capable of maintaining stability in the presence of large structural uncertainties as well as changing structural characteristics. In this work the performance of Model Reference Adaptive Control - (MRAC) is studied in numerical simulations and verified experimentally, to understand how differences between the plant and the reference model affect the control effort. MRAC is applied analytically and experimentally to a single-degree-of-freedom system and analytically to a multi-degree-of-freedom system with multi-inputs and multi-outputs. Good experimental and analytical agreement is demonstrated in control experiments and it is shown that MRAC does an excellent job of controlling the structures and achieving the desired performance even when large differences between the plant and ideal reference model exist. However, it is shown that reasonable differences between the reference model and the plant significantly increase the required control effort. The effects of increased damping in the reference model are considered, and it is shown that requiring the controller to provide increased damping actually decreases the required control effort when differences between the plant and reference model exist. This result is very useful because one of the first attempts to counteract the increased control effort due to differences between the plant and reference model might be to require less damping, however, this would actually increase the control effort. The use of optimization to successfully improve performance and reduce control effort is shown to be limited, because the actual control-structure system can not realize all the performance improvements of the analytical optimal system. Finally, it is shown that very large sampling rates may be required to accurately implement MRAC. / Ph. D.

A few problems of designing structural control systems are addressed, considering optimization of three design objectives: state error energy, control energy and stability robustness. Tradeoff relationships among these selected design objectives are investigated by solving multiple objective optimization problems. Various measures of robustness (tolerance of model errors and disturbances) are also reviewed carefully in the present study and throughout the dissertation, robust control design methodologies are emphasized. Presented in the first part of the dissertation are three new feedback design algorithms: 1) a generalized linear-quadratic regulator (LQR) formulation, 11) a generalized LQR formulation based on Lyapunov stability theorem, and 111) an eigenstructure assignment method using Sylvester's equation. The performance of these algorithms for multi-criterion optimizations are compared by generating three dimensional surfaces of wh1ch d1splay the tradeoff among the three design objectives. In the second part, a noniterative robust e1genstructure assignment algorithm via a projection method is introduced. This algorithm produces a fairly well-conditioned eigenvector matrix and provides an excellent starting solution for optimizations of various design criteria. We also present a specialized version of the projection method for second order differential equatlons, wh1ch offers useful insights to design strategies in regards to conditioning (robustness) of the eigenvectors. Finally, to illustrate the ideas presented in this study, we adopt numerical examples in two sets: 1) 6th order mass-spring systems and 11) various reduced order models of a flexible system. The numerical results confirm that multi-criterion optimizations by using a minimum correction homotopy technique is a useful tool with significant potential for enhanced computer—aided design of control systems. The proposed robust eigenstructure assignment algorithm is successfully implemented and tested for a 24th reduced order model, which establishes the approach to be applicable to systems of at least moderate dimensionality. We show analytically and computationally that constraining closed—loop eigenvectors to equal open-loop eigenvectors generally does not lead to either optimal conditioning (robustness) of the closed-loop eigenvectors or minimum gain norm. / Ph. D. / incomplete_metadata

This thesis examines the use of a linear DC motor as a proof mass actuator for the control of large space structures. A model for the actuator, including the current and force compensation used, is derived. Because of the force compensation, the actuator is unstable when placed on a structure. Relative position feedback is used for actuator stabilization. This method of compensation couples the actuator to the mast in a feedback configuration. Three compensator designs are proposed. The physical limits of the LDCM place limits on the bandwidth of the closed loop actuator. A ten mode finite element model of a flexible space structure was used in simulations to examine all aspects of the actuator's performance. The performance of the actuator is compared for the three compensator designs. The actuator bandwidth is seen to be important in the actuator's effectiveness. Increasing actuator bandwidth resulted in a saturation nonlinearity in the actuator. The excitation capability of the actuator was examined to determine the authority of the actuator. The damping of the mast modes was examined to determine the effect of the feedback configuration of the actuator/mast system. Root locus techniques were used to explain changes in the vibrational modes of the structure due to the actuator compensation. Disturbance analysis was performed to quantify the effect of corrupted measurements on the purity of force generated by the actuator. / Master of Science

Recent demands in large space structure technology have suggested the use of active control actuators integral to a structures' construction. The concept of a 3-D (triangular cross-sectioned) active truss is presented. The linear equations of motion for one plane of the truss are derived. A model for a generic flexible beam is then appended to the planar truss model. A linear time-invariant optimal control law is found, followed by a presentation of an experimental planar truss built to test the concept. Physical parameters are then substituted into the dynamic model and several sets of control gains are found. The "Kalman'' gains are applied to the experimental structure. Experimental results are compared to expected theoretical results with good (30%) correlation. Conclusions are drawn and suggestions are made for further research. / Master of Science

The analytical study presented here is concerned with by two types of sensitivity of active vibration control of large space structures (LSS). The first one required for assessing robustness, is the sensitivity of the performance and stability of the control system to changes in structure and to model reduction. The second type is the sensitivity of the optimum design of the control system to changes in the structure. This sensitivity is of interest in assessing the need for integrated structure/control design. Three direct rate feedback (DRF) control techniques are studied for a laboratory structure which has characteristics of LSS and then compared to standard linear quadratic (LQ) control. The baseline design of each control system is obtained first and then sensitivity analysis conducted. An uncoupled DRF control law which minimized the sum of gains subject to requirements on performance was not robust to structural changes, and small changes in the structure caused notable increase in performance compared to that of the baseline design and therefore a potential gain from simultaneous structure/control design was indicated. Two coupled DRF techniques are proposed. A Minimum Force DRF (MF-DRF) law minimized maximum force of any actuator, while a Linear Quadratic DRF (LQ-DRF) law minimized the standard quadratic performance index for initial conditions in the shape of the first six natural modes. Both techniques guaranteed system stability. The LQ control law was found to be only slightly better than the simpler MF·DRF law in terms of the quadratic performance index and poorer than the LQ-DRF law. However the LQ control requires model reduction and was found to be sensitive to errors in that process. For example, the LQ design lost its stability when the structure was modified by adding a non-structural mass to it. A separate experimental study was conducted simultaneously with this study to verify theoretical results. Good agreement was found between analytical results and experimental measurements for the investigated control techniques. / Ph. D.

Active control of large flexible space structures is typically implemented to control only a few known elastic modes. Linear Quadratic Regulators (LQR) and Kalman-Bucy Filter (KBF) observers are usually designed to control the desired modes of vibration. Higher modes, referred to as residual modes, are generally ignored in the analysis and may be excited by the controller to cause a net destabilizing effect on the system. This is referred to as the spillover phenomenon. This dissertation considers the stabilization of the neglected dynamics of the higher modes of vibration. It aims at designing modal controllers with improved spillover stability properties. It is based on the premise that the structural dynamicist will be able to predict more vibration modes than would be practical to include in the design of the controller. The proposed method calls for designing the observer so as to improve spillover stability with minimum loss in performance. Two formulations are pursued. The first is based on optimizing the noise statistics used in the design of the Kalman-Bucy Filter. The second optimizes directly the gain matrix of the observer. The influence of the structure of the plant noise intensity matrix of the Kalman-Bucy Filter on the stability margin of the residual modes is demonstrated. An optimization procedure is presented which uses information on the residual modes to minimize spillover (i.e., maximize the stability margin) of known residual modes while preserving robustness vis-à-vis the unknown dynamics. This procedure selects either the optimum plant noise intensity matrix or the optimum observer gain matrix directly to maximize the stability margins of the residual modes and properly place the observer poles. The proposed method is demonstrated for both centralized and decentralized modal control. / Ph. D.

Deployable structures serve a large number of space missions. They are vital since spacecraft are launched by placing them inside launch vehicle payload fairings of limited volume. Traditional spacecraft design often involves large components. These components could have power, communication, or optics applications and include booms, masts, antennas, and solar arrays. Different stowing methods are used in order to reduce the overall size of a spacecraft. Some examples of stowing methods include simple articulating, more complex origami inspired folding, telescoping, and rolling or wrapping. Wrapping of a flexible component could reduce the weight by eliminating joints and other components needed to enable some of the other mechanisms. It also is one of the most effective methods at reducing the compaction volume of the stowed deployable. In this study, a generic unfurlable structure is optimized for maximum natural frequency at its fully deployed configuration and minimal strain energy in its stowed configuration. The optimized stowed structure is then deployed in simulation. The structure consists of a rectangular panel that tightly wraps around a central cylindrical hub for release in space. It is desired to minimize elastic energy in the fully wrapped panel and hinge to ensure minimum reaction load into the spacecraft as it deploys in space, since that elastic energy stored at the stowed position transforms into kinetic energy when the panel is released and induces a moment in the connected spacecraft. It is also desired to maximize the fundamental frequency of the released panel as a surrogate for the panel having sufficient stiffness. Deployment dynamic analysis of the finite element model was run to ensure satisfactory optimization formulation and results. / Master of Science / Spacecraft, or artificial satellites, do not fly from earth to space on their own. They are launched into their orbits by placing them inside launch vehicles, also known as carrier rockets. Some parts or components of spacecraft are large and cannot fit in their designated space inside launch vehicles without being stowed into smaller volumes first. Examples of large components on spacecraft include solar arrays, which provide power to the spacecraft, and antennas, which are used on satellite for communication purposes. Many methods have been developed to stow such large components. Many of these methods involve folding about joints or hinges, whether it is done in a simple manner or by more complex designs. Moreover, components that are flexible enough could be rolled or wrapped before they are placed in launch vehicles. This method reduces the mass which the launch vehicle needs to carry, since added mass of joints is eliminated. Low mass is always desirable in space applications. Furthermore, wrapping is very effective at minimizing the volume of a component. These structures store energy inside them as they are wrapped due to the stiffness of their materials. This behavior is identical to that observed in a deformed spring. When the structures are released in space, that energy is released, and thus, they deploy and try to return to their original form. This is due to inertia, where the stored strain energy turns into kinetic energy as the structure deploys. The physical analysis of these structures, which enables their design, is complex and requires computational solutions and numerical modeling. The best design for a given problem can be found through numerical optimization. Numerical optimization uses mathematical approximations and computer programming to give the values of design parameters that would result in the best design based on specified criterion and goals. In this thesis, numerical optimization was conducted for a simple unfurlable structure. The structure consists of a thin rectangular panel that wraps tightly around a central cylinder. The cylinder and panel are connected with a hinge that is a rotational spring with some stiffness. The optimization was solved to obtain the best values for the stiffness of the hinge, the thickness of the panel, which is allowed to vary along its length, and the stiffness or elasticity of the panel's material. The goals or objective of the optimization was to ensure that the deployed panel meets stiffness requirement specified for similar space components. Those requirements are set to make certain that the spacecraft can be controlled from earth even with its large component deployed. Additionally, the second goal of the optimization was to guarantee that the unfurling panel does not have very high energy stored while it's wrapped, so that it would not cause large motion the connected spacecraft in the zero gravity environments of space. A computer simulation was run with the resulting hinge stiffness and panel elasticity and thickness values with the cylinder and four panels connected to a structure representing a spacecraft. The simulation results and deployment animation were assessed to confirm that desired results were achieved.

O presente trabalho aborda alguns aspectos estruturais e construtivos das estruturas metálicas espaciais. Inicialmente apresentam-se um breve histórico deste sistema estrutural, algumas informações gerais a respeito das classificações das estruturas espaciais, das \'tipologias\' para alguns dos sistemas mais utilizados, assim como exemplos de aplicação destas estruturas. A seguir discutem-se aspectos relativos à análise estrutural, com a apresentação de um breve roteiro de cálculo para uma cobertura em treliça espacial. Finalmente apresentam-se alguns resultados teóricos e experimentais relativos a barras comprimidas de inércia variável ao longo do comprimento. / In this work, some structural and constructional aspects of metal space structures are presented. lnitially, a brief review of this structural system is described together with some general informations about classifications, types and applications of usual systems. In addition, some aspects about structural analysis are discussed, presenting a brief guide for a space truss design. Finally, some theoretical and experimental results are illustrated for a case of axial compression members with variable stiffness.